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3 Changes between GAP 4.4 and GAP 4.5
3.1 Changes in the core GAP system
3.1-1 Improved functionality
3.1-2 Changes in distribution formats
3.1-3 Improvements to the user interface
3.1-4 Better documentation
3.2 Packages in GAP 4.5
3.2-1 Interface between the core system and packages
3.2-2 New and updated packages since GAP 4.4.12
3.3 GAP 4.5.5 (July 2012)
3.4 GAP 4.5.6 (September 2012)
3.5 GAP 4.5.7 (December 2012)

### 3 Changes between GAP 4.4 and GAP 4.5

This chapter lists most important changes between GAP 4.4.12 and the first public release of GAP 4.5. It also contains information about subsequent update releases for GAP 4.5. It is not meant to serve as a complete account on all improvements; instead, it should be viewed as an introduction to GAP 4.5, accompanying its release announcement.

#### 3.1 Changes in the core GAP system

In this section we list most important new features and bugfixes in the core system introduced in GAP 4.5. For the list of changes in the interface between the core system and packages as well as for an overview of new and updated packages, see Section 3.2.

##### 3.1-1 Improved functionality

Performance improvements:

- The GAP kernel now uses GMP (GNU multiple precision arithmetic library, http://gmplib.org/) for faster large integer arithmetic.

- Improved performance for records with large number of components.

- Speedup of hash tables implementation at the GAP library level.

- `MemoryUsage` (Reference: MemoryUsage) is now much more efficient, in particular for large objects.

- Speedups in the computation of low index subgroups, Tietze transformations, calculating high powers of matrices over finite fields, `Factorial` (Reference: Factorial), etc.

New and improved kernel functionality:

- By default, the GAP kernel compiles with the GMP and readline libraries. The GMP library is supplied with GAP and we recommend that you use the version we supply. There are some problems with some other versions. It is also possible to compile the GAP kernel with the system GMP if your system has it. The readline library must be installed on your system in advance to be used with GAP.

- Floating point literals are now supported in the GAP language, so that, floating point numbers can be entered in GAP expressions in a natural way. Support for floats is now properly documented, see Reference: Floats. GAP has an interface using which packages may add new floating point implementations and integrate them with the parser. In particular, we expect that there will soon be a package that implements arbitrary precision floating point arithmetic.

- The Mersenne twister random number generator has been made independent of endianness, so that random seeds can now be transferred between architectures. See Reference: GlobalMersenneTwister for details.

- Defaults for `-m` and `-o` options have been increased. Changes have been made to the way that GAP obtains memory from the Operating System, to make GAP more compatible with C libraries. A new `-s` option has been introduced to control or turn off the new behaviour, see Reference: Command Line Options.

- The filename and lines from which a function was read can now be recovered using `FilenameFunc` (Reference: FilenameFunc), `StartlineFunc` (Reference: StartlineFunc) and `EndlineFunc` (Reference: EndlineFunc). This allows you, for example, to implement a function such as `PageSource` (Reference: PageSource) to show the file containing the source code of a function or a method in a pager, see `Pager` (Reference: Pager).

- `CallFuncList` (Reference: CallFuncList) was made into an operation so that it can be used to define behaviour of a non-function when called as a function.

- Improvements to the cyclotomic number arithmetic for fields with large conductors.

- Better and more flexible viewing of some large objects.

- Opportunity to interrupt some long kernel computations, e.g. multiplication of compressed matrices, intercepting `Ctrl-C` in designated places in the kernel code by means of a special kernel function for that purpose.

- `ELM_LIST` now allows you to install methods where the second argument is NOT a positive integer.

- Kernel function `DirectoryContents` (Reference: DirectoryContents) to get the list of names of files and subdirectories in a directory.

- Kernel functions for Kronecker product of compressed matrices, see `KroneckerProduct` (Reference: KroneckerProduct).

New and improved library functionality:

- Extensions of data libraries:

  - Functions and iterators are now available to create and enumerate simple groups by their order up to isomorphism: `SimpleGroup` (Reference: SimpleGroup), `SmallSimpleGroup` (Reference: SmallSimpleGroup), `SimpleGroupsIterator` (Reference: SimpleGroupsIterator) and `AllSmallNonabelianSimpleGroups` (Reference: AllSmallNonabelianSimpleGroups).

  - See also packages CTblLib, IRREDSOL and Smallsemi listed in Section 3.2-2.

- Many more methods are now available for the built-in floating point numbers, see Reference: Floats.

- The bound for the proper primality test in `IsPrimeInt` (Reference: IsPrimeInt) increased up to \(10^{18}\).

- Improved code for determining transversal and double coset representatives in large groups.

- Improvements in `Normalizer` (Reference: Normalizer) for \(S_n\).

- Smith normal form of a matrix may be computed over arbitrary euclidean rings, see `NormalFormIntMat` (Reference: NormalFormIntMat).

- Improved algorithms to determine the subgroup lattice of a group, as well as the function `DotFileLatticeSubgroups` (Reference: DotFileLatticeSubgroups) to save the lattice structure in `.dot` file to view it e.g. with GraphViz.

- Special teaching mode which simplifies some output and provides more basic functionality, see Reference: Teaching Mode.

- Functionality specific for use in undergraduate abstract algebra courses, e.g. checksums (Reference: Check Digits); string/integer list conversion; rings of small orders; the function `SetNameObject` (Reference: SetNameObject) to set display names for objects for more informative examples, e.g. constructing groups from "named" objects, such as, for example, `R90` for a 90-degree rotation).

- Functions `DirectoryDesktop` (Reference: DirectoryDesktop) and `DirectoryHome` (Reference: DirectoryHome) which provide uniform access to default directories under Windows, Mac OS X and Unix.

- Improved methods for hashing when computing orbits.

- Functionality to call external binaries under Windows.

- Symplectic groups over residue class rings, see `SymplecticGroup` (Reference: SymplecticGroup).

- Basic version of the simplex algorithm for matrices.

- New functions, operations and attributes: `PrimeDivisors` (Reference: PrimeDivisors), `Shuffle` (Reference: Shuffle) for lists, `IteratorOfPartitions` (Reference: IteratorOfPartitions), `IteratorOfCombinations` (Reference: IteratorOfCombinations), `EnumeratorOfCombinations` (Reference: EnumeratorOfCombinations) and others.

- The behaviour of `Info` (Reference: Info) statements can now be configured per info class, this applies to the way the arguments are printed and to the output stream, see Reference: Info Functions.

- New function `Test` (Reference: Test) which is a more flexible and informative substitute of `ReadTest` (Reference: ReadTest) operation.

- `ConnectGroupAndCharacterTable` is replaced by more robust function `CharacterTableWithStoredGroup` (Reference: CharacterTableWithStoredGroup).

Many problems in GAP have have been fixed, among them the following:

- Polynomial factorisation over rationals could miss factors of degree greater than \(deg(f)/2\) if they have very small coefficients, while the cofactor has large coefficients.

- `IntermediateSubgroups` (Reference: IntermediateSubgroups) called on a group and a normal subgroup did not properly calculate maximal inclusion relationships.

- `CentreOfCharacter` (Reference: CentreOfCharacter) and `ClassPositionsOfCentre` (Reference: ClassPositionsOfCentre (for a character)) called for a group character could return a perhaps too large result.

- `Trace` (Reference: Traces of field elements and matrices) called for an element of a finite field that was created with `AlgebraicExtension` (Reference: AlgebraicExtension) ran into an error.

- `IrreducibleRepresentationsDixon` (Reference: IrreducibleRepresentationsDixon) did not accept a list with one character as a second argument.

- Composing a homomorphism from a permutation group to a finitely presented group with another homomorphism could give wrong results.

- For certain arguments, the function `EU` (Reference: EU) returned wrong results.

- In the table of marks of cyclic groups, `NormalizersTom` (Reference: NormalizersTom) value was wrong.

- The function `PermChars` (Reference: PermChars) returned a perhaps wrong result when the second argument was a positive integer (not a record) and the trivial character of the character table given as the first argument was not the first in the list of irreducibles.

- GAP crashed when the intersection of ranges became empty.

- `IsPSL`, and in turn `StructureDescription` (Reference: StructureDescription), erroneously recognised non-PSL groups of the right order as PSL.

- The semidirect product method for pcgs computable groups sometimes tried to use finite presentations which were not polycyclic. This usually happened when the groups were not pc groups, and there was a very low risk of getting a wrong result.

- The membership test for a group of finite field elements ran into an error if the zero element of the field was given as the first argument.

- Constant polynomials were not recognised as univariate in any variable.

- The kernel recursion depth counter was not reset properly when running into many break loops.

- GAP did not behave well when printing of a (large) object was interrupted with `Ctrl-C`. Now the object is no longer corrupted and the indentation level is reset.

Potentially incompatible changes:

- The zero polynomial now has degree `-infinity`, see `DegreeOfLaurentPolynomial` (Reference: DegreeOfLaurentPolynomial).

- Multiple unary `+` or `-` signs are no longer allowed (to avoid confusion with increment/decrement operators from other programming languages).

- Due to changes to improve the performance of records with large number of components, the ordering of record components in `View`'ed records has changed.

- Due to improvements for vectors over finite fields, certain objects have more limitations on changing their base field. For example, one can not create a compressed matrix over \(GF(2)\) and then assign an element of \(GF(4)\) to one of its entries.

No longer supported:

- Completion files mechanism.

- GAP 3 compatibility mode.

In addition, we no longer recommend using the GAP compiler `gac` to compile GAP code to C, and may withdraw it in future releases. Compiling GAP code only ever gave a substantial speedup for rather specific types of calculation, and much more benefit can usually be achieved quite easily by writing a small number of key functions in C and loading them into the kernel as described in `LoadDynamicModule` (Reference: LoadDynamicModule). The `gac` script will remain available as a convenient way of compiling such kernel modules from C.

Also, the following functions and operations were made obsolete: `AffineOperation`, `AffineOperationLayer`, `FactorCosetOperation`, `DisplayRevision`, `ProductPol`, `TeXObj`, `LaTeXObj`.

##### 3.1-2 Changes in distribution formats

The GAP 4.5 source distribution has the form of a single archive containing the core system and the most recent "stable" versions of all currently redistributed packages. There are no optional archives to download: the TomLib package now contains all its tables of marks in one archive; we do not provide separate versions of manuals for Internet Explorer, and the former `tools` archive is now included as an archive in the `etc` directory. To unpack and install the archive, user the script `etc/install-tools.sh`.

We no longer distribute separate bugfix archives when the core GAP system changes, or updated packages archives when a redistributed package is updated. Instead, the single GAP source distribution archive will be labelled by the version of the core GAP system and also by a timestamp. This archive contains the core system and the stable versions of the relevant packages on that date. To upgrade, you simply replace the whole directory containing the GAP installation, and rebuild binaries for the GAP kernel and packages. For new versions of packages, we will also continue to redistribute individual package archives so it will be possible to update a single package without changing the rest of the GAP installation.

Furthermore, by default GAP will now automatically read a user-specific GAP root directory (unless GAP is called with the `-r` option). All user settings can be made in that directory, so there will be no risk of them being lost during an update (see Section 3.1-3 below for more details). Private packages can also be installed in this directory for the same reason.

There are some changes in archive formats used for the distribution: we continue to provide `.tar.gz`, `.tar.bz2` and `-win.zip` archives. We have added `.zip`, and stopped providing `.zoo` archives. We no longer provide GAP binaries for Mac OS 9 (Classic) any more. For installations from source on Mac OS X one may follow the instructions for UNIX.

With the release of GAP 4.5, we also encourage more users to take advantage of the increasingly mature binary distributions which are now available. These include:

- The binary `rsync` distribution for GAP on Linux PCs with i686 or x86_64 compatible processors provided by Frank Lübeck, see http://www.math.rwth-aachen.de/~Frank.Luebeck/gap/rsync.

- BOB, a tool for Linux and Mac OS X to download and build GAP and its packages from source provided by M. Neunhöffer: http://www-groups.mcs.st-and.ac.uk/~neunhoef/Computer/Software/Gap/bob.html.

- The GAP installer for Windows provided by Alexander Konovalov: http://www.gap-system.org/ukrgap/wininst/.

In the near future, we also hope to have a binary distribution for Mac OS X.

Internally, we now have infrastructure to support more robust and frequent releases, and an improved system to fetch and test new versions of the increasingly large number of packages. The Example package documents technical requirements for packages, many of which are checked automatically by our systems. This will allow us to check the compatibility of packages with the system and with other packages more thoroughly before publishing them on the GAP website.

##### 3.1-3 Improvements to the user interface

By default, GAP now uses the readline library for command line editing. It provides such advantages as working with unicode terminals, nicer handling of long input lines, improved TAB-completion and flexible configuration. For further details, see Reference: Editing using the readline library.

We have extended facilities for user interface customisation. By default GAP automatically scans a user specific GAP root directory (unless GAP is called with the `-r` option). The name of this user specific directory depends on the operating system and is contained in `GAPInfo.UserGapRoot`. This directory can be used to tell GAP about personal preferences, to load some additional code, to install additional packages, or to overwrite some GAP files, see Reference: GAP Root Directories. Instead of a single `.gaprc` file we now use more flexible setup based on two files: `gap.ini` which is read early in the startup process, and `gaprc` which is read after the startup process, but before the first input file given on the command line. These files may be located in the user specific GAP root directory `GAPInfo.UserGapRoot` which by default is the first GAP root directory, see Reference: The gap.ini and gaprc files. For compatibility, the `.gaprc` file is still read if the directory `GAPInfo.UserGapRoot` does not exist. See Reference: The former .gaprc file for the instructions how to migrate your old setup.

Furthermore, there are functions to deal with user preferences, for example, to specify how GAP's online help is shown or whether the coloured prompt should be used. Calls to set user preferences may appear in the user's `gap.ini` file, as explained in Reference: Configuring User preferences.

In the Windows version, we include a new shell which uses the mintty terminal in addition to the two previously used shells (Windows command line and RXVT). The mintty shell is now recommended. It supports Unicode encoding and has flexible configurations options. Also, GAP under Windows now starts in the `%HOMEDRIVE%%HOMEPATH%` directory, which is the user's home directory. Besides this, a larger workspace is now permitted without a need to modify the Windows registry.

Other changes in the user interface include:

- the command line history is now implemented at the GAP level, it can be stored on quitting a GAP session and reread when starting a new session, see Reference: The command line history.

- `SetPrintFormattingStatus("stdout",false);` may be used to switch off the automatic line breaking in terminal output, see `SetPrintFormattingStatus` (Reference: SetPrintFormattingStatus).

- GAP supports terminals with up to 4096 columns (extendable at compile time).

- Directories in `-l` command-line option can now be specified starting with `~/`, see Reference: Command Line Options.

- Large integers are now displayed by a short string showing the first and last few digits, and the threshold to trigger this behaviour is user configurable (call `UserPreference("MaxBitsIntView")` to see the default value).

- The GAP banner has been made more compact and informative.

- `SetHelpViewer` (Reference: SetHelpViewer) now supports the Google Chrome browser.

- Multiple matches in the GAP online help are displayed via a function from the Browse package, which is loaded in the default configuration. This feature can be replaced by the known pager using the command

      SetUserPreference( "browse", "SelectHelpMatches", false );

##### 3.1-4 Better documentation

The main GAP manuals have been converted to the GAPDoc format provided by the GAPDoc package by Frank Lübeck and Max Neunhöffer (http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc). This documentation format is already used by many packages and is now recommended for all GAP documentation.

Besides improvements to the documentation layout in all formats (text, PDF and HTML), the new GAP manuals incorporate a large number of corrections, clarifications, additions and updated examples.

We now provide two HTML versions of the manual, one of them with MathJax (www.mathjax.org) support for better display of mathematical symbols. Also, there are two PDF versions of the manual - a coloured and a monochrome one.

Several separate manuals now became parts of the GAP Reference manual. Thus, now there are three main GAP manual books:

- GAP Tutorial (see Tutorial: Preface)

- GAP Reference manual (see Reference: Preface)

- GAP - Changes from Earlier Versions (this manual)

Note that there is no index file combining these three manuals. Instead of that, please use the GAP help system which will search all of these and about 100 package manuals.

#### 3.2 Packages in GAP 4.5

Here we list most important changes affecting packages and present new or essentially changed packages. For the changes in the core GAP system, see Section 3.1.

##### 3.2-1 Interface between the core system and packages

The package loading mechanism has been improved. The most important new feature is that all dependencies are evaluated in advance and then used to determine the order in which package files are read. This allows GAP to handle cyclic dependencies as well as situations where package A requires package B to be loaded completely before any file of package A is read. To avoid distortions of the order in which packages will be loaded, package authors are strongly discouraged from calling `LoadPackage` (Reference: LoadPackage) and `TestPackageAvailability` (Reference: TestPackageAvailability) in a package code in order to determine whether some other package will be loaded before or together with the current package - instead, one should use `IsPackageMarkedForLoading` (Reference: IsPackageMarkedForLoading). In addition, there is now a better error management if package loading fails for packages that use the new functionality to log package loading messages (see `DisplayPackageLoadingLog` (Reference: DisplayPackageLoadingLog) and the rest of the Chapter Reference: GAP Packages which documents how to use GAP packages), and package authors are very much encouraged to use these logging facilities.

In GAP 4.4 certain packages were marked as autoloaded and would be loaded, if present, when GAP started up. In GAP 4.5, this notion is divided into three. Certain packages are recorded as needed by the GAP system and others as suggested, in the same way that packages may need or suggest other packages. If a needed package is not loadable, GAP will not start. Currently only GAPDoc is needed. If a suggested package is loadable, it will be loaded. Typically these are packages which install better methods for Operations and Objects already present in GAP. Finally, the user preferences mechanism can be used to specify additional packages that should be loaded if possible. By default this includes most packages that were autoloaded in GAP 4.4.12, see `ShowUserPreferences` (Reference: ShowUserPreferences).

GAP packages may now use local namespaces to avoid name clashes for global variables introduced in other packages or in the GAP library, see Reference: Namespaces for GAP packages.

All guidance on how to develop a GAP package has been consolidated in the Example package which also contains a checklist for upgrading a GAP package to GAP 4.5, see Example: Guidelines for Writing a GAP Package.

##### 3.2-2 New and updated packages since GAP 4.4.12

At the time of the release of GAP 4.4.12 there were 75 packages redistributed with GAP (including the TomLib which was distributed in the core GAP archive). The first public release of GAP 4.5 contains precisely 99 packages.

The new packages that have been added to the redistribution since the release of GAP 4.4.12 are:

- Citrus package by J.D. Mitchell for computations with transformation semigroups and monoids (this package is a replacement of the Monoid package).

- cvec package by M. Neunhöffer, providing an implementation of compact vectors over finite fields.

- fwtree package by B. Eick and T. Rossmann for computing trees related to some pro-\(p\)-groups of finite width.

- GBNP package by A.M. Cohen and J.W. Knopper, providing algorithms for computing Grobner bases of noncommutative polynomials over fields with respect to the "total degree first then lexicographical" ordering.

- genss package by M. Neunhöffer and F. Noeske, implementing the randomised Schreier-Sims algorithm to compute a stabiliser chain and a base and a strong generating set for arbitrary finite groups.

- HAPprime package by P. Smith, extending the HAP package with an implementation of memory-efficient algorithms for the calculation of resolutions of small prime-power groups.

- hecke package by D. Traytel, providing functions for calculating decomposition matrices of Hecke algebras of the symmetric groups and \(q\)-Schur algebras (this package is a port of the GAP 3 package Specht 2.4 to GAP 4).

- Homalg project by M. Barakat, S. Gutsche, M. Lange-Hegermann et al., containing the following packages for the homological algebra: homalg, ExamplesForHomalg, Gauss, GaussForHomalg, GradedModules, GradedRingForHomalg, HomalgToCAS, IO_ForHomalg, LocalizeRingForHomalg, MatricesForHomalg, Modules, RingsForHomalg and SCO (see http://homalg.math.rwth-aachen.de/).

- MapClass package by A. James, K. Magaard and S. Shpectorov to calculate the mapping class group orbits for a given finite group.

- recogbase package by M. Neunhöffer and A. Seress, providing a framework to implement group recognition methods in a generic way (suitable, in particular, for permutation groups, matrix groups, projective groups and black box groups).

- recog package by M. Neunhöffer, A. Seress, N. Ankaralioglu, P. Brooksbank, F. Celler, S. Howe, M. Law, S. Linton, G. Malle, A. Niemeyer, E. O'Brien and C.M. Roney-Dougal, extending the recogbase package and provides a collection of methods for the constructive recognition of groups (mostly intended for permutation groups, matrix groups and projective groups).

- SCSCP package by A. Konovalov and S. Linton, implementing the Symbolic Computation Software Composability Protocol (SCSCP, see http://www.symbolic-computation.org/scscp) for GAP, which provides interfaces to link a GAP instance with another copy of GAP or other SCSCP-compliant system running locally or remotely.

- simpcomp package by F. Effenberger and J. Spreer for working with simplicial complexes.

- Smallsemi package by A. Distler and J.D. Mitchell, containing the data library of all semigroups with at most 8 elements as well as various information about them.

- SymbCompCC package by D. Feichtenschlager for computations with parametrised presentations for finite \(p\)-groups of fixed coclass.

Furthermore, some packages have been upgraded substantially since the GAP 4.4.12 release:

- Alnuth package by B. Assmann, A. Distler and B. Eick uses an interface to PARI/GP system instead of the interface to KANT (thanks to B. Allombert for the GP code for the new interface and help with the transition) and now also works under Windows.

- CTblLib package (the GAP Character Table Library) by T. Breuer has been extended by many new character tables, a few bugs have been fixed, and new features have been added, for example concerning the relation to GAP's group libraries, better search facilities, and interactive overviews. For details, see the package manual.

- DESIGN package by L.H. Soicher:

  - The functions `PointBlockIncidenceMatrix`, `ConcurrenceMatrix`, and `InformationMatrix` compute matrices associated with block designs.

  - The function `BlockDesignEfficiency` computes certain statistical efficiency measures of a \(1-(v,k,r)\) design, using exact algebraic computation.

- Example package by W. Nickel, G. Gamble and A. Konovalov has a more detailed and up-to-date guidance on developing a GAP package, see Example: Guidelines for Writing a GAP Package.

- FR package by L. Bartholdi now uses floating-point numbers to compute approximations of rational maps given by their group-theoretical description.

- The GAPDoc package by F. Lübeck and M. Neunhöffer provides various improvements, for example:

  - The layout of the text version of the manuals can be configured quite freely, several standard "themes" are provided. The display is now adjusted to the current screen width.

  - Some details of the layout of the HTML version of the manuals can now be configured by the user. All manuals are available with and without MathJax support for display of mathematical formulae.

  - The text and HTML versions of manuals make more use of unicode characters (but the text version is also still reasonably good on terminals with latin1 or ASCII encoding).

  - The PDF version of the manuals uses better fonts.

  - Of course, there are various improvements for authors of manuals as well, for example new functions `ExtractExamples` (GAPDoc: ExtractExamples) and `RunExamples` (GAPDoc: RunExamples) for automatic testing and correcting of manual examples.

- Gpd package by E.J. Moore and C.D. Wensley has been substantially rewritten. The main extensions provide functions for:

  - Subgroupoids of a direct product with complete graph groupoid, specified by a root group and choice of rays.

  - Automorphisms of finite groupoids - by object permutations; by root group automorphisms; and by ray images.

  - The automorphism group of a finite groupoid together with an isomorphism to a quotient of permutation groups.

  - Homogeneous groupoids (unions of isomorphic groupoids) and their morphisms, in particular homogeneous discrete groupoids: the latter are used in constructing crossed modules of groupoids in the XMod package.

- GRAPE package by L.H. Soicher:

  - With much help from A. Hulpke, the interface between GRAPE and `dreadnaut` is now done entirely in GAP code.

  - A 32-bit `nauty/dreadnaut` binary for Windows (XP and later) is included with GRAPE, so now GRAPE provides full functionality under Windows, with no installation necessary.

  - Graphs with ordered partitions of their vertices into "colour-classes" are now handled by the graph automorphism group and isomorphism testing functions. An automorphism of a graph with colour-classes is an automorphism of the graph which additionally preserves the list of colour-classes (classwise), and an isomorphism from one graph with colour-classes to a second is a graph isomorphism from the first graph to the second which additionally maps the first list of colour-classes to the second (classwise).

  - The GAP code and old standalone programs for the undocumented functions `Enum` and `EnumColadj` have been removed as their functionality can now largely be handled by current documented GAP and GRAPE functions.

- IO package by M. Neunhöffer:

  - New build system to allow for more flexibility regarding the use of compiler options and adjusting to GAP 4.5.

  - New functions to access time like `IO_gettimeofday`, `IO_gmtime` and `IO_localtime`.

  - Some parallel skeletons built on `fork` like: `ParListByFork`, `ParMapReduceByFork`, `ParTakeFirstResultByFork` and `ParWorkerFarmByFork`.

  - `IOHub` objects for automatic I/O multiplexing.

  - New functions `IO_gethostbyname` and `IO_getsockname`.

- IRREDSOL package by B. Höfling now covers all irreducible soluble subgroups of \(GL(n,q)\) for \(q^n < 1000000\) and primitive soluble permutation groups of degree \(< 1000000\) (previously, the bound was \(65536\)). It also has faster group recognition and adds a few omissions for \(GL(3,8)\) and \(GL(6,5)\).

- ParGAP package by G. Cooperman is now compiled using a system-wide MPI implementation by default to facilitate running it on proper clusters. There is also an option to build it with the MPINU library which is still supplied with the package (thanks to P. Smith for upgrading ParGAP build process).

- OpenMath package by M. Costantini, A. Konovalov, M. Nicosia and A. Solomon now supports much more OpenMath symbols to facilitate communication by the remote procedure call protocol implemented in the SCSCP package. Also, a third-party external library to support binary OpenMath encoding has been replaced by a proper implementation made entirely in GAP.

- Orb package by J. Müller, M. Neunhöffer and F. Noeske:

  There have been numerous improvements to this package:

  - A new fast implementation of AVL trees (balanced binary trees) in C.

  - New interface to hash table functionality and implementation in C for speedup.

  - Some new hash functions for various object types like transformations.

  - New function `ORB_EstimateOrbitSize` using the birthday paradox.

  - Improved functionality for product replacer objects.

  - New "tree hash tables".

  - New functionality to compute weak and strong orbits for semigroups and monoids.

  - `OrbitGraph` for Orb orbits.

  - Fast C kernel methods for the following functions:

    `PermLeftQuoTransformationNC`, `MappingPermSetSet`, `MappingPermListList`, `ImageSetOfTransformation`, and `KernelOfTransformation`.

  - New build system to allow for more flexibility regarding the use of compiler options and to adjust to GAP 4.5.

- RCWA package by S. Kohl among the new features and other improvements has the following:

  - A database of all 52394 groups generated by 3 class transpositions of \(ℤ\) which interchange residue classes with modulus less than or equal to 6. This database contains the orders and the moduli of all of these groups. Also it provides information on what is known about which of these groups are equal and how their finite and infinite orbits on \(ℤ\) look like.

  - More routines for investigating the action of an rcwa group on \(ℤ\). Examples are a routine which attempts to find out whether a given rcwa group acts transitively on the set of nonnegative integers in its support and a routine which looks for finite orbits on the set of all residue classes of \(ℤ\).

  - Ability to deal with rcwa permutations of \(ℤ^2\).

  - Important methods have been made more efficient in terms of runtime and memory consumption.

  - The output has been improved. For example, rcwa permutations are now `Display`'ed in ASCII text resembling LaTeX output.

- The XGAP package by F. Celler and M. Neunhöffer can now be used on 64-bit architectures (thanks to N. Eldredge and M. Horn for sending patches). Furthermore, there is now an export to XFig option (thanks to Russ Woodroofe for this patch). The help system in XGAP has been adjusted to GAP 4.5.

- Additionally, some packages with kernel modules or external binaries are now available in Windows. The `-win.zip` archive and the GAP installer for Windows include working versions of the following packages: Browse, cvec, EDIM, GRAPE, IO and orb, which were previously unavailable for Windows users.

Finally, the following packages are withdrawn:

- IF package by M. Costantini is unmaintained and no longer usable. More advanced functionality for interfaces to other computer algebra systems is now available in the SCSCP package by A. Konovalov and S. Linton.

- Monoid package by J. Mitchell is superseded by the Citrus package by the same author.

- NQL package by R. Hartung has been withdrawn by the author.

#### 3.3 GAP 4.5.5 (July 2012)

Fixed bugs which could lead to crashes:

- For small primes (compact fields) `ZmodnZObj(r,p)` now returns the corresponding FFE to avoid crashes when compacting matrices. [Reported by Ignat Soroko]

Other fixed bugs:

- Fixed a bug in `CommutatorSubgroup` (Reference: CommutatorSubgroup) for fp groups causing infinite recursion, which could, for example, be triggered by computing automorphism groups.

- Previously, the list of factors of a polynomial was mutable, and hence could be accidentally corrupted by callers. Now the list of irreducible factors is stored immutable. To deal with implicit reliance on old code, always a shallow copy is returned. [reported by Jakob Kroeker]

- Computing high powers of matrices ran into an error for matrices in the format of the cvec package. Now the library function also works with these matrices. [reported by Klaus Lux]

- The pseudo tty code which is responsible for spawning subprocesses has been partially rewritten to allow more than 128 subprocesses on certain systems. This mechanism is for example used by ANUPQ and nq packages to compute group quotients via an external program. Previously, on Mac OS X this could be done precisely 128 times, and then an error would occur. That is, one could e.g. compute 128 nilpotent quotients, and then had to restart GAP to compute more. This also affected other systems, such as OpenBSD, where it now also works correctly.

- On Mac OS X, using GAP compiled against GNU readline 6.2, pasting text into the terminal session would result in this text appearing very slowly, with a 0.1 sec delay between each "keystroke". This is not the case with versions 6.1 and older, and has been reported to the GNU readline team. In the meantime, we work around this issue in most situations by setting `rl_event_hook` only if `OnCharReadHookActive` is set.

- `ShowUserPreferences` (Reference: ShowUserPreferences) ran into a break loop in case of several undeclared user preferences. [Reported by James Mitchell]

- GAP did not start correctly if the user preference `"InfoPackageLoadingLevel"` was set to a number \( >= 3\). The reason is that `PrintFormattedString` was called before it was installed. The current fix is a temporary solution.

- The `"hints"` member of `TypOutputFile` used to contain 3*100 entries, yet `addLineBreakHint` would write entries with index up to and including 3*99+3=300, leading to a buffer overflow. This would end up overwriting the `"stream"` member with -1. Fixed by incrementing the size of `"hints"` to 301. [Reported by Jakob Kroeker]

- The function `IsDocumentedWord` tested the given word against strings obtained by splitting help matches at non-letter characters. This way, variable names containing underscores or digits were erroneously not regarded as documented, and certain substrings of these names were erroneously regarded as documented.

- On Windows, an error occurred if one tried to use the default Windows browser as a help viewer (see `SetHelpViewer` (Reference: SetHelpViewer)). Now the browser opens the top of the correspoding manual chapter. The current fix is a temporary solution since the problem remains with the positioning at the required manual section.

Improved functionality:

- `WriteGapIniFile` (Reference: WriteGapIniFile) on Windows now produces the `gap.ini` file with Windows style line breaks. Also, an info message is now printed if an existing `gap.ini` file was moved to a backup file `gap.ini.bak`.

- The CTblLib and TomLib packages are removed from the list of suggested packages of the core part of GAP. Instead they are added to the default list of the user preference `"PackagesToLoad"`. This way it is possible to configure GAP to not load these packages via changing the default value of `"PackagesToLoad"`.

- The conjugacy test in \(S_n\) for intransitive subgroups was improved. This deals with inefficiency issue in the case reported by Stefan Kohl.

- Added `InstallAndCallPostRestore` to `lib/system.g` and call it in `lib/init.g` instead of `CallAndInstallPostRestore` for the function that reads the files listed in GAP command line. This fixes the problem reported by Yevgen Muntyan when `SaveWorkspace` (Reference: SaveWorkspace) was used in a file listed in GAP command line (before, according to the documentation, `SaveWorkspace` (Reference: SaveWorkspace) was only allowed at the main GAP prompt).

- There is now a new user preference `PackagesToIgnore`, see `SetUserPreference` (Reference: SetUserPreference). It contains a list of names of packages that shall be regarded as not available at all in the current session, both for autoloading and for later calls of `LoadPackage` (Reference: LoadPackage). This preference is useful for testing purposes if one wants to run some code without loading certain packages.

#### 3.4 GAP 4.5.6 (September 2012)

Improved functionality:

- The argument of `SaveWorkspace` (Reference: SaveWorkspace) can now start with `~/` which is expanded to the users home directory.

- Added the method for `Iterator` (Reference: Iterator) for `PositiveIntegers` (Reference: PositiveIntegers). [Suggested by Attila Egri-Nagy].

- Changed kernel tables such that list access functionality for `T_SINGULAR` objects can be installed by methods at the GAP level.

- In case of saved history, "UP" arrow after starting GAP yields last stored line. The user preference `HistoryMaxLines` is now used when storing and saving history (see `SetUserPreference` (Reference: SetUserPreference)).

Fixed bugs which could lead to crashes:

- A crash occuring during garbage collection following a call to `AClosVec` for a `GF(2)` code. [Reported by Volker Braun]

- A crash when parsing certain syntactically invalid code. [Reported by multiple users]

- Fixed and improved command line editing without readline support. Fixed a segfault which could be triggered by a combination of "UP" and "DOWN" arrows. [Reported by James Mitchell]

- Fixed a bug in the kernel code for floats that caused a crash on SPARC Solaris in 32-bit mode. [Reported by Volker Braun]

Other fixed bugs:

- Very large (more than 1024 digit) integers were not being coded correctly in function bodies unless the integer limb size was 16 bits. [Reported by Stefan Kohl]

- An old variable was used in assertion, causing errors in a debugging compilation. [Reported by Volker Braun]

- The environment variable `PAGER` is now correctly interpreted when it contains the full path to the pager program. Furthermore, if the external pager `less` is found from the environment it is made sure that the option `-r` is used (same for `more -f`). [Reported by Benjamin Lorenz]

- Fixed a bug in `PermliftSeries`. [Reported by Aiichi Yamasaki]

- Fixed discarder function in lattice computation to distinguish general and zuppo discarder. [Reported by Leonard Soicher]

- The `GL` (Reference: GL (for dimension and a ring)) and `SL` (Reference: SL (for dimension and a ring)) constructors did not correctly handle `GL(filter,dim,ring)`.

- The names of two primitive groups of degree 64 were incorrect.

- The `\in` (Reference: \in operation for testing membership) method for groups handled by a nice monomorphism sometimes could produce an error in situations where it should return false. This only happened when using `SeedFaithfulAction` to influence how `NiceMonomorphism` (Reference: NiceMonomorphism) builds the nice monomorphims for a matrix groups.

- Wrong `PrintObj` (Reference: PrintObj) method was removed to fix delegations accordingly to Reference: View and Print.

- Fixed a method for `Coefficients` (Reference: Coefficients) which, after Gaussian elimination, did not check that the coefficients actually lie in the left-acting-domain of the vector space. This could lead to a wrong answer in a vector space membership test. [Reported by Kevin Watkins]

Improved documentation:

- Removed outdated statements from the documentation of `StructureDescription` (Reference: StructureDescription) which now non-ambiguosly states that `StructureDescription` is not an isomorphism invariant: non-isomorphic groups can have the same string value, and two isomorphic groups in different representations can produce different strings.

- GAP now allows overloading of a loaded help book by another one. In this case, only a warning is printed and no error is raised. This makes sense if a book of a not loaded package is loaded in a workspace and then GAP is started with a root path that contains a newer version. [Reported by Sebastian Gutsche]

- Provided a better description of user preferences mechanism (Reference: Configuring User preferences) and a hint to familiarise with them using `WriteGapIniFile` (Reference: WriteGapIniFile) function to create a file which contains descriptions of all known user preferences and also sets those user preferences which currently do not have their default value. One can then edit that file to customize (further) the user preferences for future GAP sessions.

New packages added for the redistribution with GAP:

- AutoDoc package by S. Gutsche, providing tools for automated generation of GAPDoc manuals.

- Convex package by S. Gutsche, which provides structures and algorithms for convex geometry.

- PolymakeInterface package by T. Baechler and S. Gutsche, providing a link to the callable library of the polymake system (http://www.polymake.org).

- ToolsForHomalg package by M. Barakat, S. Gutsche and M. Lange-Hegermann, which provides some auxiliary functionality for the homalg project (http://homalg.math.rwth-aachen.de/).

#### 3.5 GAP 4.5.7 (December 2012)

Fixed bugs which could lead to crashes:

- Closing with `LogInputTo` (or `LogOutputTo`) a logfile opened with `LogTo` (Reference: LogTo) left the data structures corrupted, resulting in a crash.

- On 32-bit systems we can have long integers `n` such that `Log2Int(n)` is not an immediate integer. In such cases `Log2Int` gave wrong or corrupted results which in turn could crash GAP, e.g., in `ViewObj(n)`.

- Some patterns of use of `UpEnv` (Reference: UpEnv) and `DownEnv` (Reference: DownEnv) were leading to a segfault.

Other fixed bugs:

- Viewing of long negative integers was broken, because it went into a break loop.

- Division by zero in `ZmodnZ` (Reference: ZmodnZ) (\(n\) not prime) produced invalid objects. [Reported by Mark Dickinson]

- Fixed a bug in determining multiplicative inverse for a zero polynomial.

- Fixed a bug causing infinite recursion in `NaturalHomomorphismByNormalSubgroup` (Reference: NaturalHomomorphismByNormalSubgroup).

- A workaround was added to deal with a package method creating pcgs for permutation groups for which the entry `permpcgsNormalSteps` is missing.

- For a semigroup of associative words that is not the full semigroup of all associative words, the methods for `Size` (Reference: Size) and `IsTrivial` (Reference: IsTrivial) called one another causing infinite recursion.

- The 64-bit version of the `gac` script produced wrong (>= 2^31) CRC values because of an integer conversion problem.

- It was not possible to compile GAP on some systems where `HAVE_SELECT` detects as false.

- Numbers in memory options on the command line exceeding 2^32 could not be parsed correctly, even on 64-bit systems. [Reported by Volker Braun]

New packages added for the redistribution with GAP:

- Float package by L. Bartholdi, which extends GAP floating-point capabilities by providing new floating-point handlers for high-precision real, interval and complex arithmetic using MPFR, MPFI, MPC or CXSC external libraries. It also contains a very high-performance implementation of the LLL (Lenstra-Lenstra-Lovász) lattice reduction algorithm via the external library FPLLL.

- ToricVarieties package by S. Gutsche, which provides data structures to handle toric varieties by their commutative algebra structure and by their combinatorics.

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